When my father dropped off a couple of battered polystyrene bodyboards he'd found in a shed last summer we had only the most optimistic thoughts of using them and no inkling at all of how within a few weeks we'd be chasing the lotus, the dream, the storm, or whatever it is surfers restlessly chase searching the ultimate high: a journey that would take us over the water to a remote, deserted island, a place where we would whoop with delight in the delirious tumble of blue ocean; where we would be – very nearly – swept out to sea; where we would cook sausages.

This vision seemed so improbable not because we don't live by the sea – we can see it from our upstairs windows – but because that particular bit of sea hardly ever has surf. North Norfolk's beaches shelve imperceptibly for miles. Go for a swim when the tide is out and… well, you'll just walk until you're closer to Skegness than where you left your clothes and still only your shins will be wet. This achingly gradual incline of sand does for any self-respecting wave. They don't so much thunder as whisper. They're mouse waves, inching up the shore.

Unless you get the timing just right, as we did by accident one evening when we found a stiff northerly chasing the very apex of the tide over the last few yards of beach before the dunes at Holme. Here the sand does shelve enough to induce more of a bang than a whimper, and for an hour the problem was not so much the surf as that there were only two boards and four of us. The waves were easy to catch and we skimmed over them. It was wild fun.

Addicted, we bought two more boards and for days watched the weather and the tides, waiting for our stars to align. They never did. One evening, in desperation, we went anyway and tried to surf 2in waves. It was properly crap in a way only the east coast can be. I needed only a knotted hankie on my head and a crab on my toe. The family became restless. What we craved was a beach where the distance between high tide and low was a few hundred yards, not a few miles. Should we drive to Cornwall?

And then I remembered Scolt Head. The last time, we had gone over there in a friend's dinghy and walked over the dunes through bracken and brambles and marram grass, climbing all the time until we stood 50ft above the water, a tumbling cliff of sand ahead of us and then open sea. There were fat rollers that day, I was sure of it, and water that faded to deep blue, not endless brown. Scolt Head is the best we can do for an island in north Norfolk, but we'd find surfing there for sure.

Formed by the ceaseless, complex drifts of wind-blown sand over those vast, exposed beaches, the dunes of the north coast of Norfolk have grown slowly over many years: restless, shape-shifting, unstable. The fingerprints of their growth are obvious in the satellite images on Google Earth, as are the fractal replicas echoed along the coast, elongated commas of sand stretching east to west: Blakeney Point, the sands off Holkham, Gun Hill. All the creeks turning left.

Only Scolt Head makes an island though, because the tidal creeks encircle it from Burnham Overy Staithe to Brancaster. Four miles of wild and lonely dunes, scrub, open beach, breaking waves and saltmarsh, Scolt Head is so many thousand acres of one of the most important and beautiful wildlife reserves on the east coast. You're not exactly encouraged to run all over it. There are no campsites, though I've heard adventurous folk have slept there, only the stars for company. Respect is the word. This is a place to leave as you find it, a place to tread lightly. But it is accessible. In the summer a ferry runs there from Burnham Overy. Or you can take a two-mile stroll to Gun Hill and swim the channel – 50 yards and best done at the slack of the tide. Or you can sail.

Every high tide through the summer the water is abuzz with sailing dinghies peopled by hearty water-bobs, and the odd poop-poop speedboat. For an angler, though, I am defiantly un-nautical: the best taxi I could offer my surf-hungry kids was a canoe. We launched at Burnham Overy. We had sausages on board, Ribena, crisps and a dog. Two bodyboards. Some people audibly admired our bravery and pluck. Into the running tide and a stiff north-westerly it was slow going. At times I wasn't sure we were actually moving. Dinghies fizzed about us like wasps. The poop-poopers motored blithely by, long gone before their ferocious wakes had the canoe bouncing dangerously in the chop. But we stayed afloat and finally, finally made it, grinding up the sand about an hour after we set off. At more or less the same time a water-taxi dumped a platoon of tourists alongside us. "I thought you said a canoe was the only way to get here," said the daughter of mine who hadn't paddled.

The surf, though, was worth every stroke of the oar. Somehow we got it just right, as the tide, wind and sand combined to turn a healthy swell into rolling blue fairground rides. It wasn't Hawaii. None of us was quite Laird Hamilton. But who gives? Say 'aloha' slowly enough and you too can sound like Bernard Matthews.

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